Cathode follower



Dec. 20, 1960 J. R. MACDONALD 2,965,852

CATHODE FOLLOWER Filed OCt. 25. 1954 3 Sheets-Sheet 1 output tube INVENTOR Jams Ross Macdom/d BY Maw ATTORNEYS Dec. 20, 1960 J. R. MACDONALD 2,965,852

CATHODE FOLLOWER Filed 001;. 25. 1954 3 Sheets-Sheet 2 v 30.9 A E 20.8 1 D E: 0'! o THEORETICAL LINE 0 EXPERIMENTAL POINTSA N l 3 w 2 1 g 0.5 04

TOTAL LOAD RESISTANCE R (OHMS) THEORETICAL LINE EXPERIMENTAL POINTS NORMALIZED ERROR VOLTAGE /e |o I02 lo :0 FIG. 3 TOTAL LOAD RESISTANCE RL(OHMS) INVENTOR James flax: Macdma/d BY Mf /M ATTORNEYS Dec. 20, 1960 J. R. MACDONALD 2,9

CATHODE FOLLOWER I Filed Oct. 25. 1954 s Sheeis-Sheet :5

2o -zoo IO I00 OUTPUT TUBE Z LOAD o PEAK CURRENT O: o L (mu) U) 5 g FEQ T cu EN 2 PARALLEL PAARUAGLMLEENLTED AUGMENTED Q CFD CFD 0 E n: x LL! 1 E NO LOAD o I PARALLEL '5 x AUGMENTED w I CFD o 1 SERIES n: I AUGMENTED if I CFD so AND 5600 CPS I MIXED 4:l I I l I l l oil I I I l l I I 30 4o so so 10 so 90 I00 F G 5 DRIVER OUTPUT VOLTAGE (rmsVOLTS) INVENTOR James Kass Macdona/d BY WWI/W ATTORNEYS United States Patent CATHODE FOLLOWER James Ross Macdonald, Dallas, Tex., assignor to Texas Instruments Incorporated, Dallas, Tex., a corporation of Delaware Filed Oct. 25, 1954, Ser. No. 464,335

3 Claims. (Cl. 330-91) This invention relates to an improved type of cathode follower for connecting a high impedance source to a low impedance load. More specifically, this invention relates to a cathode follower circuit and a method wherein the voltage dllference between the input voltage and the output voltage is amplified and fed back in such a manner as to reduce the output impedance of the cathode follower and, in addition, reduce distortion in the output voltage.

In the prior art there are several well-known devices for connecting the voltage developed across a high impedance source to a low impedance load. One of these devices is a transformer in which the primary side is impedance-matched to the source and the secondary side is impedance-matched to the load by winding each side with the number of turns of wire required to provide the necessary impedance transformation ratio. The number of turns on the secondary then is smaller than the number of turns on the primary and is in a proportion to the primary turns as the square root of the ratio of the impedance of the source to the impedance of the load. Such a device is known as a step-down transformer and, according to transformer theory, the voltage in the secondary is to the voltage in the primary as the number of turns in the secondary is to the number of turns in the primary. Consequently, in a step-down transformer, the voltage in the secondary is reduced in direct proportion to the ratio of the number of secondary turns to the number of primary turns and thus, such a device is undesirable for use in connecting a high impedance source to a low impedance load. In addition to voltage reduction from the primary to the secondary, transformers have a limited frequency response and, in applications where it is desired to feed back part of the output voltage to reduce distortion, vinterstage transformers tend to limit the amount of negative feedback which may beremployed. v

Another meanswell-known in the art for connecting the voltage developed across a high impedance source to a low impedance load is the cathode follower, discussions of which can be found in Applied Electronics by Gray, Second edition, pp. 428-435; Radio Engineering by Terman, pp. 308-311; and Electronic Engineering Principles by Ryder, pp. 179-183. In a cathode follower circuit, the plate load impedance is eliminated and voltage is developed across the cathode resistor and thus follows the voltage applied to the grid. An analysis of the cathode follower circuit reveals two important features. First, its voltage amplification, e /em, ap: proaches ,u./(,u.+1) as the load impedance becomes very large. Thus, the. maximum voltage amplification obtainable is somewhat less than ,unity and the cathode follower is, therefore, not useful as a voltage amplifier. Second,

its internal output impedance which the load faces is approximately l' /(/L+1) and approaches 1/35,, as p becomes large compared with unity. As a consequence of this small output impedance, the cathode follower is useful for supplying a low impedance load and hence finds extensive application as an impedance transformer between a source having a high impedance and a load having a low impedance. By virtue of the fact that it is possible for the output voltage to almost approach the input voltage, the cathode follower avoids the voltage loss inherent in the step-down transformer and has the added advantages of excellent frequency response, high input impedance and low distortion. Further, even though it lacks voltage amplification, the cathode follower can provide power amplification because the ratio of its input impedance to its output impedance is very large.

However, in spite of the general usefulness of the cathode follower as an impedance transformer, there arecertain limitations to its usewhich must be considered.- One limitation on the cathode follower is that, for a given; AC. input voltage, the cathode follower output begins to be clipped on negative peaks when the output load impedance is sufiiclently low that the peak A.C. current through the output load equals the quiescent current in; the cathode follower load resistance. This follows from a consideration of the fact that if the load impedance is sufiiciently low, the current through the tube flows mainly through the load impedance rather than the cathode load resistance. Since the current through the cathode reslstance follows the voltage swings of the grid, the cur rent through the load resistance is limited to the quiescent" current through the cathode load resistance until the tube reaches its cutoff point and the negative peak volt-; ages are then clipped at that level. Another limitationis that, on positive A.C. voltage peaks, the cathode follower can deliver positive current peaks far larger than its quiescent cathode current, but the output voltage begins to be distorted when the current required by the load produces an internal voltage drop across the effective iniernal resistance l/g which is appreciable compared to the input voltage. Thus, with a load whose value. depends on the voltage across it, larger and larger per centages of the input voltage appear across the internal resIstance as the load increases while smaller and smaller percentages appear across the load. This distortion can; be partly compensated by employing overall negative feedback around the entire circuit so that in the region of appreciable positive grid current on the output tube where the follower tends to limit on positive peaks, this feedback increases the grid voltage of the cathode follower and thus its output to reduce limiting on positive voltage peaks. The limits to this-method of correction arise mainly from the limited voltage swing and distortion generation of the tube preceeding the cathode follower. In many types of circuits, such as audio amplifier cir-- cuits, it is very desirable to transfer power to the output tubes at a high efiiciency. Among the many ways inwhlch high power transfer at high efficiency can be ac-- compllshed, one method is to operate the output tubes in either class A A8 or B amplification; but allof' these modes of operation require that the grids'of the output tubes be driven positive and draw grid current during part of each cycle. In the ordinary cathode follower, the fact that the cathode follower output begins to be clipped on negative peaks when the load impedance is sufiiciently low is of no consequence when the cathode follower is used as a driver stage since the load presented by the grid of the output tube will be very small until the output tube grid potential is driven near-and above zero. The distortion, though, of the cathode follower. output voltage as the current required by the load begins to produce an appreciable voltage drop across the effect've internal resistance I/g is important since the positive .gridcurrent whichit can supply to an output tube 0 gridds limited. Therefore, the present invention has been conceived to overcome some of the limitations on the use of the cathode follower as an impedance trans former and thus constitutes an improved type of cathode follower.

This invention consists essentially of a tube with a resistor connected in the cathode path to ground or to a fixed negative potential as in the ordinary cathode follower and an additional tube connected either in parallel or in series with the first tube. The input voltage is applied to the grid of the first tube thereby producing an output voltage which is very nearly equal to but smaller than that of the input voltage. The difference between the input and output voltages is then fed to a differential amplifier and this amplified error voltage applied to the grid of either the parallel or series connected tube and with such a phase sense that the error at the output of the first tube is reduced. The feedback is thus negative feedback and augments the cathode follower, or in other words, reduces its output impedance and the distortion in its output voltage. It should be noted here that, although the invention is described herein in terms of vacuum-tubes, suitable transistors such as field-effect transistors can be used to build up the improved cathode follower driver of this invention and achieve the same reduced output impedance and reduced output voltage distortion.

Accordingly, it is the principal object of this invention to augment the impedance transforming characteristics of the cathode follower in such a manner that the output impedance of the cathode follower will be further decreased thereby making it suitable for use in a circuit between a high impedance source and an extremely low impedance load.

It is another principal object of this invention to provide negative feedback to reduce distortion in the output voltage thereby increasing the circuit stability. In conjunction with this object, a negative feed-back path is provded for the au mented cathode follower driver which is essentially outside of the main amplification path of any circuit in which it might be used. With such a separate active error feed-back path, greater overall feedback than might otherwise be possible may be used to greatly reduce distortion throughout the circuit.

It is a further object of this invention to provide an augmented cathode follower driver which may be used for direct coupling to and biasing of output tubes in either single-ended or push-pull circuits.

It is a still further object of this invention to provide an augmented cathode follower that can considerably augment the range of loads over which an essentially undistorted output voltage can be maintained and in particular, loads consisting of a grid which draws high positive grid current during a potion of a cycle.

The above objects of the present invention will be clarified and other objects made known from the following discussion when taken in conjunction with the drawings in which:

Figure 1 is a schematic circuit diagram for an augmented cathode follower wherein a tube is connected in parallel to the cathode follower;

Figure 2 is a curve of the theoretical and experimental ratio of the output voltage with total load R to the output voltage with only cathode resistance lead R plotted against the load resistance for the parallel augmented cathode fol ower driver circuit of Fi ure 1;

Figure 3 is a curve of the theoretical and experimental ratio of the error voltage normalized with respect to the input voltage plotted against load resistance for the parallel augmented cathode follower circuit of Figure 1;

Figure 4 is a schematic circuit diagram for an augmented cathode follower wherein a tube is connected in series with the cathode follower; and

Figure 5 is a plot of the intermodulation distortion against R.M.S. output voltage for an ordinar cathode follower driver, a series augmented cathode follower driver, a parallel augmented cathode follower driver all driving an output tube grid and a parallel augmented cathode follower driver with no added load.

Beginning now the description of the drawings, a parallel augmented cathode follower driver circuit is shown schematically in Figure 1. The input voltage e is fed by lead 10 to the grid of tube V1 which in this diagram is shown as one-half of a double triode tube. Tube V2, the other half of the double triode tube, is connected in parallel with tube V1 by means of lead 13 connecting the plates of the two tubes. The D.C. voltage to the plates of tubes V1 and V2 is supplied by a voltage source to the common plate connection, lead 13. Cathode resistor 11 is connected in series with tube V1 by a lead 14 and in series with tube V2 by a lead 15. The output voltage e is developed across resistor 11 and applied to a low impedance load by lead 12.

In order to augment the cathode follower action of tube V1, the input voltage 2 is fed through resistor 17 to the grid of tube V3 by lead 16 while the output voltage e is applied to the grid of tube V4 by lead 18. The cathodes of tubes V3 and V4 are connected together by a common lead 20 and in series with resistor 19. The plate of tube V3 is connected directly to a D.C. voltage source while the plate of tube V4 is connected to a second D.C. voltage source through pate load resistor 21. The circuit consisting of tube V3, tube V4, and resistors 19 and 21 provides for amplification of the difference between the input voltage e and the output voltage a in a manner described in Vacuum-tube Amplifiers, Radiation Laboratory Series, volume 18, section 11-10. Tube V3 is connected as a cathode follower and thus, the input voltage e to its grid is transmitted with very little drop to the cathode of tube V4. Tube V4, however, acts as an amplifier with its grid biassed negatively with respect to its cathode. The difference between the input voltage 2 and the output voltage e is amplified by the voltage drop gain across resistor 21 to give the amplified error signal (g e g e or, its approximate equivalent, g(e -e This error voltage provides a high stability and reduced distortion when fed back to the cathode follower V2. Further, this active error feed-back path of th au mented c"thode fol ower is Outside the main amplification path of any circuit into which it might be connected and thus allows greater overall negative feedback to be used in the entire circuit with no amplification of the distortion from stages ahead of the augmented cathode follower dri er.

The error voltage from tube V4 follows a path throu h lead 22, condenser 26 and lead 25 to the grid of tube V2. Condenser 26 provides an A.C. byp ss around resistor 23 and, since resistor 24 is of co siderab e ma nitude compared with the reactance of condenser 26 at fre uencies of interest. the error volta e feeds to the grid of tube V2 w th verv little or no voltage drop through resistor 24. The grid of tube V2 is provided with a negative D.C. bias equal to that of the negative D.C. bias on the grid of tube V1 bv means of a voltage divider consisting of resistors 23 and 24. The voltage through resistor 21 is applied to t e voltage divider and the voltage drop across resistor 23 reduces the voltage to the proper D.C. level for the grid of tube V2.

From the circuit described, it follows then that as the load reo ires more current, the output voltage e will drop. This results in an increased error voltage which is amplified and fed to the grid of the parallel connected tube V2. Since tube V2 is a cathode follower also, the voltage across res stor 11 increases to compensate for the current supplied to the load thereby reducing the error voltage. Expressing the circuit of Figure 1 by means of formulas, feeding the amplified error voltage into the parallel connected tube V2 results in a no-load voltage gain for the parallel augmented cathode follower p=amplification factor of tubes V1 and V2.

g =voltage gain from grid to plate of V4.

g =voltage gain from grid of V3 to plate of V4.

r =rlalate resistance of tubes V1 and V2, assumed identi- R =the cathode resistance of tubes V1 and V2 (resistor 11).

Since G is equivalent to g and g is approximately equal to 32 then:

and consequently it can be seen that the cathode follower of this invention is essentially augmented by the multiplication factor g.

Insofar as the voltage drop through the cathode follower is concerned, the internal resistance r, for the augmented cathode follower is approximately equal to:

#92 gm fym When compared with the internal resistance of essentially l/g for a well designed ordinary cathode follower, it can be seen that by augmenting the cathode follower, the internal resistance is reduced by the factor g. In actual output impedance, this is a reduction in the output impedance from approximately 200-400 ohms for the ordinary cathode follower to approximately 5 ohms for the parallel augmented cathode follower of Figure 1.

As a further verification of the operation of the parallel augmented cathode follower driver of Figure 1, reference is now made to the curves shown in Figures 2 and 3. In Figure 2, a curve is drawn for the ratio of the output voltage with a total load R to the output voltage with only cathode resistance load R as the value of the total load resistance R increases. The solid line representing theoretical voltage amplification shows that for low values of total load resistance the voltage amplification is comparatively small. However, as the load resistance increases, the voltage amplification increases until it approaches unity. The triangular points repre sent experimental points determined by introducing successively increasing values of load resistance across the output of the parallel augmented cathode follower. The close correspondence of the experimental points with the theoretically calculated curve shows that the theory of the augmented cathode follower driver is sound in actual practice. In Figure 3, a plot of the error voltage e normalized with respect to the input voltage e is shown for increasing values of the total load resisance R The theoretically calculated curve shown by the solid line indicates that the error voltage should be large in comparison with the input voltage for low values of load resistance and that this ratio should decrease as the load resistance increases. Again, the experimental points shown by the small triangles indicate that the actual performance of the parallel augmented cathode follower driver corresponds very closely with its theoretically calculated performance.

Another means for augmenting a cathode follower is shown by the series connection of Figure 4. In this figure, the input voltage e is fed to the grid of tube V5 throu h lead 40. The cathode of tube V5 is connected to a fixed negative potential through resistor 41. However, tube V5 is connected in series with tube V9 by the connection 50 between the plate of tube V5 and the cathode of tube V9. The output voltage e developed across resistor 41 is shown as being fed to an output tube V10 by lead 42.

As in the parallel augmented cathode follower, the difference between the input voltage e and the output voltage E; is amplified in a differential amplifier. This is accomplished by connecting the output voltage e to the grid of tube V7 through lead 43. The input voltage e is connected into the grid of a cathode follower tube V8 and the voltage drop across resistor 45 in the cathode circuit of tube V8 is fed to the grid of tube V6 by lead 46. Tubes V6 and V7 are identical halves of a double triode tube, have a common cathode connection 47 and are connected in series with lead 48 to a fixed negative potential. The difference between the halves of the double triode lies in the fact that tube V6 is a cathode follower while tube V7 is an amplifier. Thus, the difference between the voltages e and 2;; is amplified by the voltage drop across the plate load resistance 49. As in the parallel augmented cathode follower circuit of Figure 1, the gain through tube V7 is equal to (g e --g e which is essentially equal to g(e e This amplified error voltage is then fed by lead 51 to the grid of tube V9. Thus, the series augmented cathode follower is likewise provided with error feedback to increase its stability and reduce distortion and its active error feedback path is essentially out of the main amplification path of any circuit into which it might be connected.

The error voltage is applied to the grid of tube V9 by lead 51 and acts to augment the cathode follower tube V5 in the following manner. As current is supplied to a low resistance load such as the grid of the output tube V10 when driven positive, the voltage drop across the tube V5 increases. However, any internal resistance drop will be compensated by an increase in the plate voltage of tube V5 due to the error voltage (2 supplied to the grid of tube V9 by the amplified error voltage. This compensation effect continues as the load increases until the grid of tube V9 arrives at the zero bias condition for the tube. Compensation is limited at this point since there can be no further voltage drop across tube V9. Compared with the parallel augmented cathode follower circuit, the output impedance of the series augmented cathode follower is considerably higher, being in the order of 50-70 ohms as against 5 ohms for the parallel circuit. However, the series augmented cathode follower considerably augments the range of loads over which an undistorted output voltage can be maintained when compared with an ordinary cathode follower, the reduction being in the order of 200 to 400 ohms to 60 ohms.

An analysis of this series augmented cathode follower by means of its equivalent circuit shows that the no-load voltage gain from grid to cathode is approximately:

where:

g =the voltage gain from the grid of V8 to the plate of g =the voltage gain from the grid of V7 to the plate of =amplification factor of tubes V5 and V9, assumed to be identical.

Since g and g are very nearly equal and usually, in practice, considerably larger than the amplification factor G will be essentially unity. As to tube V5, its output impedance is approximately:

factor (1+g /u To illustrate the effect which augmenting the output of a cathode follower has on distortion, a series of curves are produced in Figure where the intermodulation distortion in percent for frequencies of 60 and 5600 c.p.s. mixed in the ratio of 4:1 is plotted against R.M.S. output voltage. Taking the most extreme case of distortion, the curve for an ordinary cathode follower driver (CPD) shows that the percentage of distortion is approximately 0.24% at an output voltage of 30 volts R.M.S., the point at which the output grid starts drawing positive grid current, and as the output voltage increases, the intermodulation distortion rises sharply until it is approximately 8.0% at an output of 45 volt R.M.S. The intermodulation distortion increases at a lesser rate from that point on until the diode line of the tube is reached and there the distortion increases sharply. The diode line is reached when the grid of the output tube is sufficiently positive that it loses control of plate current and the tube then begins to act as a diode. The curve for the series augmented cathode follower driver (SACFD) shows considerable distortion over the range between approximately 30 volts R.M.S. and the diode line but still the distortion is considerably lower than in an ordinary cathode follower driver. The curve for the parallel augmented cathode follower driver (PACFD) shows an intermodulation distortion of less than 0.2% in the range of 30 to 50 volts R.M.S. and an intermodulation distortion which never rises above 0.9% until the output voltage approaches the point at which the output tube begins to act as a diode. This latter described curve follows very closely a portion of the no-load curve for the parallel augmented cathode follower driver which represents the distortion when no output grid current is drawn. The distortion arises almost entirely from the preceding amplifier stage (not shown). Thus, it can be seen that where distortion in the output voltage is concerned, the parallel follower driver is far superior to both the series driver and the ordinary cathode follower, while the series augmented follower represents an improvement over the ordinary cathode follower driver. The dash line shows that the parallel augmented driver can deliver output grid currents up to 100 ma. with an intermodulation distortion of less than 10% in the output stage.

The present invention has been described by means of two schematic circuit diagrams showing a parallel augmented cathode follower driver and a series augmented cathode follower driver together with specific voltages, resistance values, tube types and bias conditions to illustrate the invention as actually reduced to practice. However, it is obvious to one skilled in the art that these circuits may be modified at will without departing from the purpose of this invention which is to disclose an improved type of cathode follower with any extremely low output impedance and with a minimum of distortion in the output voltage. Therefore, any changes or modifications to the circuit shown and described in this invention which can be made without departing from the objects stated herein are claimed as within the scope of this invention.

What is claimed is:

1. In an amplifier circuit, an improved circuit for reducing output impedance and output voltage distortion which comprises a vacuum tube having a grid, plate and cathode, means connecting said vacuum tube as a single stage cathode follower, said last named means including a load impedance connected to the cathode of said vacuum tube, a cathode follower means having an input and an output, means amplifying the difierence etween the input voltage at the grid of said vacuum tube and the output voltage generated across said load impedance to provide active error voltage, means feeding said active error voltage to the input of said cathode follower means, and means electrically connecting the output of said cathode follower means to augment the current flow ing through said load impedance.

2. In an amplifier circuit, an improved circuit for re ducing output impedance and output voltage distortion as defined in claim 1, said cathode follower means comprising a second vacuum tube having a grid, plate and cathode connected in parallel with said first mentioned vacuum tube plate-to-plate and cathode-to-cathodc with said active error voltage fed to the grid of said second vacuum tube.

3. In an amplifier circuit, an improved circuit for reducing output impedance and output voltage distortion as defined .in claim 1, said cathode follower means comprising a second vacuum tube having a grid, plate and cathode connect-2d in series in the plate circuit of said first mentioned vacuum tube with the cathode of said second vacuum tube connected to the plate of said first mentioned vacuum tube and with said active error voltage fed to the grid of said second vacuum tube.

References Cited in the file of this patent UNITED STATES PATENTS 2,592,193 Saunders Apr. 8, l952 2,628,266 Schroeder Feb. 10, 1953 2,647,174 Maron July 28, 1953 2,685,000 Vance July 27, 1954 2,709,205 Colls May 24, 1955 2,7l4,i36 Greenwood July 26, 1955 2,730,573 Scdgfield et al. Jan. 10, 1956 2,737,547 Deming Mar. 6, 1956 2,763,733 Coulter Sept. 13, 1956 2,795,654 Macdonald June 11, 1957 2,801 296 Blecher July 30, 1957 2,810,025 Clements Oct. 15, 1957 2,896,027 Smith July 21, 1959 FOREIGN PATENTS 620,140 Great Britain Mar. 21, 1949 

